A method for determining characteristic pressure parameters during hydraulic fracturing based on linearized fitting

XIAO Haifan; WU Ningyu; GAO Guiyun; LIU Jikun; YANG Xinshuai; HUANG Xiaopan

doi:10.12090/j.issn.1006-6616.2025091

Volume 31 Issue 6

Dec. 2025

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Article Navigation > Journal of Geomechanics > 2025 > 31(6): 1282-1295

XIAO H F，WU N Y，GAO G Y，et al.，2025. A method for determining characteristic pressure parameters during hydraulic fracturing based on linearized fitting[J]. Journal of Geomechanics，31（6）：1282−1295 doi: 10.12090/j.issn.1006-6616.2025091

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A method for determining characteristic pressure parameters during hydraulic fracturing based on linearized fitting

doi: 10.12090/j.issn.1006-6616.2025091

1.
National Institute of Natural Hazards, Ministry of Emergency Management, Beijing 100085, China
2.
School of Engineering and Technology, China University of Geosciences (Beijing), Beijing 100083, China

Funds: This research is financially supported by the National Natural Science Foundation of China (Grant No. 42174118).

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Received: 2025-07-27
Revised: 2025-10-13
Accepted: 2025-10-22

Available Online: 2025-12-02

Published: 2025-12-28

Abstract

Abstract

Objective Hydraulic fracturing is a fundamental technique for in-situ stress measurement, yet conventional methods of interpreting the instantaneous shut-in pressure (p_s) and reopening pressure (p_r) are often sensitive to noise, strongly subjective, and inadequate for facing nonlinear pressure–time responses. To address the lack of objective, robust, and high-accuracy identification methods, this study proposes a linearized curve-fitting approach capable of automatically determining key characteristic pressures from complex fracturing curves. Methods The method transforms a nonlinear pressure–time curve into multiple locally linear segments through polynomial smoothing, adaptive sliding-window regression, and statistical slope-change detection. Significant slope mutations are used to automatically identify p_s during the shut-in decay stage and p_r during the re-pressurization stage. The method is validated using true-triaxial hydraulic fracturing laboratory tests on granite and field tests at the Jizhou pumped-storage power station (75–277 m depth). Results Across six granite specimens (HF2–HF9), the proposed method consistently produced p_r values between those obtained by the single-tangent and shifted-p_b methods, avoiding the low–high systematic bias of the two techniques. For p_s, the method yielded similar or more conservative results than traditional methods, with most absolute deviations <0.40 MPa. The method demonstrated strong consistency across varying stress states and significantly reduced subjective scatter. The principal stresses calculated from p_s and p_r showed physically reasonable trends. The σ₁ errors were <30% in most cases and the behavior was stable without random jumps, indicating improved objectivity of the automated identification. In the four tested depth intervals of the LFZK02 borehole, p_r and p_s determined by traditional methods exhibited large spreads (e.g., p_r deviations >1.5 MPa and p_s deviations up to 0.74 MPa). In contrast, the linearized method consistently produced values close to the multi-method averages and with much smaller dispersion. For p_s, deviations relative to Muskat and derivative methods were typically <0.20 MPa. Using the automatically identified p_s and p_r, the derived principal stresses showed a clear horizontally compressive regime (S_H=6.55–9.85 MPa; S_h=3.54–6.21 MPa), matching regional stress data and confirming the reliability of the method in actual field conditions. Conclusion The linearized curve-fitting method effectively overcomes the subjectivity, noise sensitivity, and model-dependence of conventional hydraulic-fracturing interpretation approaches. This method provides stable, accurate, and repeatable identification of p_s and p_r in both laboratory and field environments and maintains good performance under nonlinear responses, data disturbance, and multi-cycle loading–unloading conditions. [Significance] This study offers a robust, automated, and universally applicable tool for interpreting hydraulic-fracturing pressure curves, significantly enhancing the reliability of in-situ stress measurements and supporting the development of intelligent, standardized stress-testing systems for underground engineering.
- linearized curve fitting method,
- reopening pressure (p_r),
- instantaneous shut-in pressure (p_s),
- hydraulic fracturing,
- in-situ stress measurement

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References(53)

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